The 15 Function Problem

Number Theory Level 2

Here is a sequence:

$\large \begin{cases} F(1) = 1 \\ F(2n) = F(n) \\ F(2n+1) = F(2n)+1 \end{cases}$

Which position in this sequence does the number 15 appear for the first time?

1 solution

X X
Apr 21, 2018

Express n in binary,F(n) is the digit sum of n.So the first time F(n) is 15,n=111111111111111(in binary),which equals 32767